Let T be multiplication by the matrix A, find the rank and nullity of T. 1 1 3 A = 6 7 -4 58 rank (T) nullity (T)-i

Q: y' = x - 4xy

A: We have to find solution of differential equation.

Q: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 1 = 0

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Q: Instruction: Integrate

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Q: cos² (x) + cos² (1) (x) cos³ IF .dx

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Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

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Q: Given the geometric sequence: 24, Find an explicit formula for an, where the first term is a₁ = 24.…

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Q: Consider the following function. f(x)=√x-1, (17,4) (a) Find an equation of the tangent line to the…

A: Here we have to find the equation of tangent line.

Q: H.W: Evaluate the integral 2. 01 jj(x+y+ -1-1 (x+y+1)dxdy

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Q: J sin²(x) cos(x) dx

A: We have to evaluate ∫sin2x cos2x dx.

Q: The function h is defined as follows. h(x) = x² +7x-18 x²-8x+7 Find h (4). Simplify your answer as…

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Q: T.

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Q: Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the two…

A: Given

Q: S 3 7 39+x² dx

A: We need to solve integral.

Q: 8 Given g(x) = -2x³ + x, answer the following: Part: 0/3 Part 1 of 3 (a) Find g(-x). 8 (-x) =

A: We can solve the question as below.

Q: Find the root's 51 of Complex equation:

A: Given:      5√(-1)

Q: Find positive numbers x and y satisfying the equation xy=9 such that the sum 3x+y is as small as…

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Q: If a x i = 0 and a x j = 0, then Select one: O O a is equal to k a is any vector perpendicular to i…

A: We know that if two vector are collinear then their cross product is zero, Therefore 'a x i =0 '…

Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

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Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

A: Given: Lsin2tcos3t

Q: Consider the point P(-2, 1, 4) and the vectors Question 2 a = and b =. (a) Find the unit vector u…

A: This question can be solved using the concept of three dimensional geometry.

Q: Evaluate limx→∞ 3x^2 - x - 2/ 5x^2+4x+1

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Q: dy (8) The solution of differential equation: + y = xy³ is dx (a) = x + ²+ce²ª, y (b) = x² + + ce²x,…

A: Using differential equations

Q: Question 3: A) Find the critical points of the DE: y' = y¹ − 5y³ + 4y². B) Classify each critical…

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Q: 00 To test the series Σ as is the case with all series of this type.) According to the P-test: the…

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Q: 1 A = 1 1 * The Eigen values of the matrix 0 1 1 10 1. 1 10 0,2,-1 O 0,0,1 O 0,2,2 O 0,1,2 O 0-12

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Q: Evaluate the function for the given values of x. h(x)= Part 1 of 5 h(-3)= Part 2 of 5 -5x+7 for x…

A: The given function,   hx=-5x+7for x≤-23x+2for -2<x<34for x≥3

Q: \(\) The vectors u= 8> and v= are not orthogonal if and only if -136 Select one: O True O False

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Q: Domain star tree door cloud O Function O Not a function Relation 1 O Function O Not a function Range…

A: Solution

Q: Please solve the bottom question.

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Q: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: [z(t) = 3t² y(t) =…

A: We can express x in terms in terms of y as below.

Q: n=1 nvn Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the…

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Q: 6. Evaluate lim no 3n²-7n +41 2n² +42n- en

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Q: Q5: Find the area shared by the cardioid r = 1 + cose and the circle r = 3 cos 0. Graph the two…

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Q: 3 A line passes through the point (-6, 4) and has a slope of 2 Write an equation in slope-intercept…

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Q: The alternating series E-1 (-1)" n³ 2n³+3 is diverge. True O False O

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Q: J = * By using trapezoidal rule, n=2, The integral π/2 sin (x) dx 0.9482 0.9480 0.9481 0.9444…

A: To evaluate the integral J=∫0π2sin(x)dx usiing Trapezoidal Rule:

Q: The Eigen values of the matrix A = = 1 1 li 1 0 1 1 0 0 1 0,1,2 O 0,0,1 O 0,2,-1 O 0,-1,2 O 0,2,2 O

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Q: (a) Graph f(x) = 3 x for x < 0. (b) Graph g(x) = 2√√x for x ≥ 0. (c) Graph r(x) = 3|x for x < 0 2√x…

A: Consider   a)      f(x)=3x      for x&lt;0b)      g(x)=2x      for x≥0c)       r(x)=3x          for…

Q: Suppose that the functions h and g are defined as follows. h(x)= (-5+x) (5+x) g(x)=-8-6x (a) Find…

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Q: (1) Suppose directional derivatives of the scalar function f(P) at a point P = (x, y), in the…

A: Solution: Let ∇f=xi+yj Then ∇f.3i+4j5=1⇒xi+yj.3i+4j5=1⇒3x5+4y5=1⇒3x+4y=5............(1)

Q: 9x² +4y²-24y - 72x - 144 = 0

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Q: 1. Use a trig substitution to evaluate √9-x² 3√3/2 x² -dx.

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Q: 4. 4 1 [x²ydxdy 20

A: The given double integral is;  x2y, x from 0 to 1, y from 2 to 4.

Q: What does the following equation represent in R3 -7x + 5y = 0 O Line O None of the others O Plane O…

A: What does the following equation represent in R3   -7x+5y =0

Q: Problem 3. Solve below definite integrals In(x) (a) fate" dt. (6) fated. (c)(3) dz. 3te5tdt, 31…

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Q: The equation represents Select one: x² + y² + z² + 6z = 4x + 12 a sphere with center(-2, 0, 3) and…

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Q: Problem 2. Solve these integrals using integration by parts 2x - 3 -da, er (a) [ 27 (b) logą (r)da,…

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Q: a. (f+g) (x)  the problem is f(x)=3x+4; g(x)= 2x-3

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Q: If the vectors a and b are such that |a| |b| = -5, and a b = 10, then the angle between the two…

A: We want to select the correct option.

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution: